One-dimensionality of the organic conductor (FA)+·2PF-6

Solid State Communications, Vol. 53, No. 1, pp. 7 3 - 7 6 , 1985. Printed in Gr~at Britain.

0038-1098/85 $3.00 + .00 Pergamon Press Ltd.

ONE-DIMENSIONALITY OF THE ORGANIC CONDUCTOR (FA)~" PF6 G. Sachs, E. Dormann and M. Schwoerer Physikalisches Institut, Universit/it Bayreuth, Postfach 3008, D-8580 Bayreuth, FRG

(Received 4 September 1984 by P.H. Dederichs) Proton spin lattice relaxation is analysed in the radical cation salt (FA)2PF6 for 14MHz < Vp < 200 MHz at T = 293 K. From the observed variation of T1 with frequency the time constant r* describing the interruption of the one-dimensional diffusive motion is determined. In our samples, r*-values in the range ( 2 - 4 ) " 10 -12 s were derived, depending on sample quality. Analysis of the available data gives a consistent picture of (FA)2 PF6 in its high temperature phase as a quasi-1D organic conductor whose extreme one-dimensionality is spoiled by sample imperfection. of the free induction decays adopting standard inversionrecovery technique [ 15 ]. The short FID decay constant of only about 12-15 las required that appropriate experimental care was taken to optimise rf pulse heights, receiver-bandwidth and dead time; the signal to noise ratio had to be improved by sampling making use of a fast ADC. Furthermore, the proton FID of (FA)2PF6 had to be separated from that of a spurious portion of the sample whose initial amplitude amounted to 25% in sample A or 5% in sample B. Separation was easy to achieve due to a large difference in 7"2 values respectively FID decay constants, at least for temperatures above 230 K. T1 of the spurious sample portion showed pronounced variation with frequency. The "correct" proton signal could clearly be identified by correlation of 1H-, 19F. ' 31p. and ESR-signal heights at the same frequency [5, 9]. Two sets of data were recorded for sample B: one series of measurements was performed on the freshly grown crystals sealed under nitrogen in a quartz crucible (B-fresh) whereas a second series of measurements was taken on a part of this sample two months later after repeated temperature cycles and exposure to air (B-aged). Here we report only on the frequency dependence of T1. Its dependence on temperature for Up = 14.5, 22 and 44 MHz was already reported before [5, 12]. The values of 1/T1 derived for T = 293 K are represented in Fig. 1. We also included T1 values for two orientations of the stacking axis "a" of a single crystal with respect to the external magnetic field [16] ; they were derived with help of the Overhauser shift method presented recently [ 12] ; the angular variation of T1 amounts to about 10%. The recovery curves on the polycrystalline samples were not single-exponential. The "error" bars, given in Fig. 1 take partially into account the range of Tx-values, estimated from a twoexponentials fit while the "points" correspond to the Mo'(1-2/e)-recovery. Especially for low Larmor frequencies the spread of Tl-values estimated by the two-

1. INTRODUCTION SINCE THE FIRST REPORT [1] in 1980 the stoichiometric organic conductor (Fluoranthenyl)~" PF6 as well as (FA)2-radical cation salts with other anions earned considerable experimental interest [ 2 - 1 3 ] , caused at least in part by their extremely narrow ESR line of less than 10 mGauss width in their high temperature "metallic" phase. In the electrochemically grown single crystals, the FA molecules are arranged in onedimensional stacks slightly dimerized with interplane distances al = 3.28 A and a2 = 3.33 A, respectively, (a = al + a2), and with much larger interstack separation [2]. Low frequency electrical conductivity [ 10] and optical reflectivity [13] support the picture of a one-dimensional organic metal. There is ample evidence that the ESR signal originates from the charge carriers on the pure hydrocarbon molecular stack [ 3 - 1 2 ] , whose density amounts to one per (FA): dimer. But despite the application of a wide selection of magnetic resonance techniques [ 3 - 1 2 ] , the discussion about the interactions dominating the spin dynamics as well as about the relevant time scales is still highly controversial: Estimates instead of truly derived values had to be used for the time constant describing the interruption of 1-D diffuse intrastack spin motion, caused by transverse (interstack) hopping (r±) or trapping on the same stack due to impurities (~-*). This quantity will be determined here by means of an analysis of the proton spin lattice relaxation as a function of frequency as was done e.g. in TTF-TCNQ by Soda et al. before [14]. Thus we shall establish a more reliable basis for a discussion of spin dynamics in the "metallic" high temperature phase of the one-dimensional organic conductor (FA)2PF6. 2. EXPERIMENTAL PROCEDURE AND RESULTS Proton spin lattice relaxation was determined in two different polycrystalline samples (A, B) by analysis 73

74

ONE-DIMENSIONALITY OF THE ORGANIC CONDUCTOR ( F A ) ~ ' P F g 10

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20

3o

z.o

i

i

i

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8o I

I

Ve / G H z ~z.o 18o

~oo i

i

I

T

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T = 293 K

...... ?:': .............. ::5. t "%:v;'::° 7 2 7 2 2 °. --> .... ....... i !',:2 !::ii!!'ii ..... /

I 15

t 20

30

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I 50

I 60

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I 80

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I 100

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Fig. 1. Frequency dependence of proton spin lattice relaxation in (FA)2 PF6 and comparison with predictions according to equation (1). For details see text. Experimental data from H6ptner etal. [5, 17] and Denninger etal. [12] are included. exponentials fit is much larger than 10% and thus could not be explained on the basis of the angular variation of Tx for randomly oriented crystals in the polycrystalline sample. It will become clear in the following that this spread of T1 -values reflects the spread of values for r* in the polycrystalline sample, the time constant r* describing interruption of the 1-D diffuse motion along the stack due to sample defects. The two T~-values, represented by open triangles, were extrapolated from lower temperatures to T = 293 K, using data reported by H6ptner et al. [5, 17] ; t h e y were derived at a polycrystalline sample with a somewhat different NMR technique. 3. DISCUSSION The available experimental data for (FA)2 PF6 seemed to give a consistent picture of the interstack motion as corresponding to a metal with an extremely short mean free path of the charge carriers [11]. The spin diffusion constant DI[ was derived on a single crystal by analysis of the electron spin echo decay in the/2stime-scale in the presence of a magnetic field gradient applied along the stacking direction [18]. It amounts to DII (293 K) ~ 2 c m 2 s -1 for (FA)zPF6, comparable with the value that was derived on (FA)2 AsF6 before [ 11 ]. Adopting the free electron model [11, 14] one would calculate a mean scattering time rll = 2.6 • 10 -is s from the relation DII = v~7"ll (with VF = 2.8 • l 0 s m s -1 for a one-dimensional band, filled up to one hole per (FA)2 dimer, or kv = rr/(2a) respectively [9] ). The corresponding mean free path A = VFirll = 7.3 A. is o f the

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order of the intrastack molecular spacing. This smafl mean free path time constant would be in agreement with the value of the scattering time that can be estimated from electrical conductivity [10, 11 ] : the relation oll = ne2rs/me gives rs = 1.3 • 10 -is s, if the experimental value oij (293 K) = 600 ( ~ c m ) -1 is used [10]. Hence h/% would be of the same order of magnitude as the Fermi energy EF and therefore the organic conductor (FA)2 PF6 even in its "metallic" high temperature phase - would evidently [14] reside on the bordering region of being a poor 1-D metal instead of a low mobility semiconductor [11]. Our following discussion will show, however, that this conclusion results from an oversimplified analysis: both experimental quantities, DEI and opl, are derived for a time-scale that is long as compared to the time constant describing interruption of the 1-D diffusive motion in a real sample of (FA)2 PF6. As we alluded to in the introduction, no reliable value of r± (or r*) was derived for (FA)2PF6 before. Different estimated values were proposed however, based on the general result that for high enough electron Larmor frequencies coe • r± > 1 (but w e • % "~ 1) the decay of the low-q spin correlations in a 1-D conductor is diffusive and thus spectral densities entering into linewidth- and relaxation-formulas should follow an co; 1/2law. For Larmor frequencies so small that We" r± < 1 3-D behaviour of the spin correlations and frequency independent spectral densities are to be observed. Since the ESR linewidth in (FA)2PF6 was found to be independent of frequency for ue = 10 MHz up to 9.5 GHz [4, 9], an upper limit of r± < 1.7 • 10 -11 s was obtained. A similar estimate was derived from the observation [9, 11 ] that up to Pe = 9.8 GHz the electron spin relaxation times T~ and T~ are the same. Since however variation with (Ue)-1/2 seemed to be followed at higher Larmor frequencies by the proton spin lattice relaxation rates at up = 22 and 44 MHz (open triangles in Fig. 1), estimates o f t ± = 5 • 10 -12 s and r* = 1.6. 10 -11 s respectively were suggested [5, 11]. The 1IT1 data for different samples and for the extended frequency range shown in Fig. 1 allowed for the first time a detailed fit of the relation derived by Soda et al. [14] to (FA)2PF6: (T1" T)-I = Cj(r±/r")'[ 1+211[11/211/2+ + ((.(COe'r±)2 OeT"±) 2 ]]

+ Q.

(1)

Here C1 describes those parts o f the contact AIS relaxation rate that originate from diffusive electron spin density wave contributions and which are strongly enhanced due to multiple electron-nucleus scattering in

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ONE-DIMENSIONALITY OF THE ORGANIC CONDUCTOR (FA)~'PF6

the quasi 1-D system. C2 collects those parts that are frequency independent up to frequencies beyond the range of interest like contributions from dipolar (I+_Sz) interaction or eventually nondiffusive 2kF SDW contributions. Several conclusions can be drawn already from inspection of the data without quantitative analysis: (i) for high Larmor frequencies, variation of 1/T1 with frequency approaching a (ve) -in-law is indeed observed, supporting the assumption of 1-D diffusive motion; (ii) there is a considerable sample dependent variation of 1/T1 at low frequency; (iii) for the sample with highest low frequency 1/T1, the frequency dependence of 1/Ta sets in at the lowest frequency and vice versa; (iv) when the same sample deteriorates (B fresh B aged), low frequency 1/T1 decreases and the setting in of frequency dependence is shifted to higher frequencies. Since frequency dependence sets in for We ~ 1/(2" r±) in equation (1), we have to conclude, that different values of "r±" occur in the different samples. Thus our measurement does not reflect the intrinsic or ideal value of 71, describing escape from 1-D diffusive motion due to tunneling in the perfect (FA)2 PF6 crystal structure. Instead the time constant T* characterizing the interruption of the 1-D motion due to the encounter of lattice imperfections or impurities in the real crystals is observed. As we remarked in section 2, the scatter of r* values for the polycrystalline samples and the corresponding scatter of relaxation rates also explains the non-single-exponential recovery curves. For a more quantitative discussion let us fit equation (1) to our experimental data. We get 6'2" 293 K = (0.2 +- 0.1)s -1 for all samples. Cz amounts to 10% of C1 only and resides thus at the error limit of our present analysis. This small value indicates that for (FA)2 PF6 only the dipolar part of the hyperfine interaction contributes to Ca. Both parts of the relaxation rate that result from contact hyperfine interaction - relaxation via q ~ 0 - as well as via q ~ 2kF-SDW excitations [14] must contribute to the frequency dependent part reflecting the diffusive behaviour o f these excitations. The minor role played by dipolar contributions is in agreement with the small angular variation of proton T1 in single crystals [16] and the large positive Overhauser enhancement (550, i.e. 84% of optimum) observed recently in proton dynamic nuclear polarization [181. Let us now discuss the values of C1 and r* derived here. The proton relaxation data, shown in Fig. 1, were fitted with the same value of C2 and also with all

75

other constants, entering into equation (1) being unchanged; only ~'* had to be adjusted, and values between 2.2 and 4.4 • 10 -12 s were obtained. These numbers are smaller than the earlier estimates for (FA)2 PF6 but still of the same order of magnitude as the values reported for TMTTF-TCNQ and related conductors [14]. This makes clear that at ESR frequencies above 1 8 - 3 6 GHz a typical 1-D narrowing of the ESR linewidth with frequency (re) -1/2 might be observable on samples of this quality - which is difficult to achieve since the ESR line is extremely narrow at low frequencies already and the influence of the Overhauser shift is going to increase [12]. Actually, the values of ~-* are not so far from what can be estimated from the macroscopic charge- and spincarrier diffusion constant DEI = 2 cm 2 s -1 and the concentration of low temperature paramagnetic spin S = I/2-defects of about 10 -3 per (FA)2 dimer, determined from ESR intensity [3, 8, 9] on typical samples of electrochemically grown (FA)2 PF6 : assuming that these defects in one stack as well as in the four neighbouring ones interrupt the diffusive motion we arrive at a time interval of 9 • 10 -11 s left for 1-D diffusion. If we make the reasonable assumption, however, that microscopic, truely 1-D (short time) diffusive motion is "faster" by a factor of about 20 than the longtime average DII , w e arrive at the value 4.4 • 10 -12 s observed for r*. The dependence on sample quality together with the value of T* = 4 . 4 . 10 -12 s indicates that (FA)2PF6 crystals of higher perfection eventually might show an extreme degree of one-dimensionality, as suggested on experimental grounds by Sigg et al. [7] : we can estimate the transfer-integral to be t± < 6.1 • 10 -3 eV = 2.8 • 10 -2 • EF from the relation [14] r i 1 = (2n/h). t~ (rll/h) by using the maximal value o f t * for T± and 2.6 • 10 -15 s for rlj - both being lower limits. To express the onedimensionality in terms of electrical conductivity, we can estimate o± with the help of the relation [14] o± = n o e 2 d~/(kB Tr±) = n (EF) e 2 d~ IT±. Again r* < r~ is used and we arrive at or± < 0.8 (~2cm) -1 ~ 1/740 • ollo b s . (with the nearest interstack separation d± being taken from crystal structure data [2] and n(EF) from the experimental value of the spin susceptibility [9] ). This may be compared with an experimental value of a±/o H~ 1/i00 derived for (FA)2SbF6 [10]. Finally we discuss the values of C1" 293 K = (1.85-2.6) s -1 derived here. Since the hyperfine coupling constant averaged over the 20 protons of one (FA)2 dimer, azz/gld B = - - 1 . 1 Gauss [16], and the spin susceptibility Xp = 9 4 . 10 -6 emu/(mole (FA)2 PF6 ) [9] are known, we can calculate the bare (3-D) Korringa relaxation rate [15] of the protons in (FA)2PF6. Compared with this value the observed rates C1 are larger by factors of 4 5 - 6 3 . The influence of multiple electron nucleus scattering and the enhance-

76

ONE-DIMENSIONALITY OF THE ORGANIC CONDUCTOR (FA)~" PF6

ment factors K0(c 0 a n d K2kF(O0 were analysed by Soda et al. [14] ; they lead to an increase of the relaxation rate by a factor of (r*/r,) 1/2. [Ko(~) + K2h~,(~)]/2 in 1-D systems. Ko(c~) ~ (1 -- ~)o.s ~ 0.9 may be estimated from the negligible enhancement (25%) of the static spin susceptibility compared with the free electron value [9]. K2kF(O0 should be larger due to the divergence of the Lindhard function for q = 2k F in 1-D systems. With % = 2.6 • 10 -is s (DII = 2 cm 2 s -1 ) we calculate this enhancement factor to be 2.2, roughly a factor of 7 smaller than for TTF-TCNQ [14]. We may interpret this difference as indication that tire true 1-D scattering time rap in (FA)2PF6 is larger than 2.6 • 10 -is s by a factor of about [(0.9 + 2.2 • 7)/(0.9 + 2.2)] 2, i.e. rli) ~ 7 • 10 -14 s. This would change the estimates given above into t I < 5.5 • 10 -a EF and h/r~ D = 4.3 • 10 -2 EF. The macroscopic diffusion constant DII = 2 cm 2 s -a would be explained along these lines as resulting from periods of coherent 1-D motion lasting about 7 • 10 -14 S, respectively lk = vF • rat) = 2 • 10 -~ m or about 30 lattice constants a, giving Dan = v~- ra D = 56 cm 2 s -a . After the time r* with this 1-D motion the next lattice-imperfection at ~ ~ (1.1--1.5) • 10 -7 m ~ ( 1 6 5 - 2 3 0 ) a is reached this is the end of the 1-D diffusive SDW decay discussed before. The time required to pass such a lattice defect would then decrease the macroscopic diffusion constant DII and the electrical conductivity oll to the lower values observed.

proton spin lattice relaxation's frequency dependence in X. We are indebted to G. Denninger for suggestions and H. Bromer (TU Braunschweig) for the possibility to take T~ -data at 200 MHz on his Bruker CXP 200 spectrometer. We thank K. Fesser for a critical reading of the manuscript. This work was supported by the Stiftung Volkswagenwerk. (FA)2

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

4. CONCLUDING REMARKS By an examination of the proton spin lattice relaxation we derived values of the time constant r* characterizing interruption of 1-D diffusive motion in (FA)2 PF6 "real crystals" due to lattice imperfections of about ( 2 - 4 ) • 10 -xz s. The analysis of our data indicates, that more perfect crystals of (FA)2 PF6 might show even more pronounced one-dimensional properties. A quantitative picture of proton spin lattice relaxation for our samples could be established, at least for T = 293 K. A more extended analysis of temperature, frequency and sample dependences of the proton Ta's in (FA)2PF6 has to follow, however, in order to detect possible deviations from the simple Korringa law Ta • T = const., that was reported to be obeyed in the metallic high temperature phase of (FA)2PF6 for up = 14.5, 22 and 44MHz [5, 12, 17].

l 1. 12. 13.

14. 15. 16.

17.

Acknowledgements

We thank B. Kraus and J. Gmeiner for growing the crystals and J.U.v. Schiitz (U. Stuttgart) for early discussions on the importance of studying the

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18.

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